The initial semimajor axes of the test particles are assigned with a radial volume density profile proportional to \(a^{-3.35}\)  [1]} from a minimum semimajor axis of 20,000 AU to a maximum semimajor axis of 50,000 AU. The maximum semimajor axis is motivated by the very short dynamical lifetimes of Oort cloud measured beyond this semimajor axis [2]}. The minimum semimajor axis is less physically motivated. Although virtually all models of Oort cloud formation predict a substantial population of bodies interior to \(a<20,000\)  AU [3]}, [4]}, [5]}, [2]}, the one major observational constraint on the Oort cloud's properties comes from the (predominantly near-Earth) LPC catalog. Although an Oort cloud population interior to \(a<20,000\)  AU can generate these observed LPCs, it is not strictly necessary to explain their existence. Meanwhile, our initial interest in distant LPC fading arose from the observed paucity of distant LPCs (\(8<q<12\)  AU) with semimajor axes below \(\sim \) 10\(^4\)  AU. From prior work, it is clear that bodies in the inner 20,000 AU of the Oort cloud will dramatically enhance the production of distant LPCs with \(a<\sim \) 10\(^4\)  AU. This means that inclusion of \(a<20,000\)  AU orbits in our initial conditions would greatly increase the chance that LPC fading is required to bring our simulations into agreement with observations, and while unphysical, the choice to exclude \(a<20,000\)  AU Oort cloud orbits is a conservative one with respect to LPC fading.
